Best Day Trips from Florence?

First off, don't make the mistake of spending your limited time in Florence on a train going to other places. You could easily spend the 4 days not even seeing half of Florence & all it has to offer. That being said, a nice half-day trip could be to Fiesole, the hilltown that overlooks Florence. Leave late morning from La Pira near Piazza San Marco on bus #7, buying round trip tickets at any nearby tabacchi shop. Sit on the right side of the bus as it climbs the hill. After about 30 minutes, you arrive in medieval Fiesole. Have a leisurely lunch at Ristorante La Reggia degli Etruschi www.lareggiadeglietruschi.com for wonderful Tuscan fare, tour the town and catch the bus back after a couple hours. Very enjoyable!

Another vote for lovely Fiesole - here's more info:
The hilltop church of San Francesco has a good view of Florence and the plain below from its terrace and benches. Halfway up the hill you'll see sloping steps to the right; they lead to a lovely wooded park with trails that loop out and back to the church. If you really want to stretch your legs, walk 4 km (2½ mi) back toward Florence center along Via Vecchia Fiesolana, a narrow lane in use since Etruscan times, to the church of San Domenico. Sheltered in the church is the Madonna and Child with Saints by Fra Angelico, who was a Dominican friar here. Piazza San Domenico, off Via Giuseppe Mantellini, Fiesole, Italy. PHONE: 055/59230. OPEN: Daily 9-noon. It's only a five-minute walk northwest from the church of San Domenico to the Badia Fiesolana, which was the original cathedral of Fiesole. Parts of it date from the 11th century, but it was substantially enlarged after 1456. Via della Badia dei Roccettini 11, Fiesole, Italy. PHONE: 055/59155. OPEN: Weekdays 9-6, Sat. 9:30-12:30.

Ravenna and the Cinque Terre are a bit of a distance from Florence (about 2.5 hrs and 3 hrs respectively by train). They are both doable, however there are many other famous places in Tuscany which are much closer. I'll mention some of the most popular (in parenthesis the public transportation mode- avg travel time).

SHORT TRIPS:
Fiesole (city bus - 20 min). You can do this in just an afternoon/evening.
Pistoia (train - 30 min)

EACH ONE IS AN ALL DAY TRIP:
1-Siena (bus -70min)
2-Pisa (train - 50 to 90 min) and Lucca (train, 25 min from Pisa or 75 min from Florence)
3-San Gimignano (bus or train+bus - 2 hrs) and Certaldo (near San Gimignano, then train back to Florence from Certaldo, or the exact opposite).
4-Chianti Hills tour (bus - ~1 hr or private car tour)
5-Arezzo (train-1hr) and Cortona (train-20 min further south than Arezzo). Do Cortona first, then Arezzo on the way back to Florence.

Florence is extremely dense in things to see and do; if you aren't interested in the Renaissance art heritage of Florence, I wouldn't bother staying there at all. It is a pretty expensive base for not planning to be there. I totally disagree with wasting a day in Fiesole with so little time in Florence. I have spent many weeks in Florence and still felt the day in Fiesole was distinctly low on the list of memorable times. There is an interesting old ampitheater (we once went to an opera there) but if you only have time for one day trip, I would choose Siena Fiesole is an expensive suburb of Florence. The views of Florence are much better from the other side at Piazale Michelangelo and the little church of San Miniato is a must see for us.

In Florence I would not pass up the old Monastery at San Marco where Savanrarola lived and ruled and Fra Angelico painted devotional frescoes in the monk's cells, or Santa Maria del Carmine where Massacio began the Rennaisance, or Santa Maria Novela, Santa Croce and the Duomo Baptistry. I'd definitely want to visit the Academia for David and the Uffizi and climb the Duomo. And that is just the short list.

Siena is an easy daytrip from Florence via bus and the Cathedral is jawdropping inside and climbing the Torre Mangia for a view out over town and country is spectacular.

3 nights in Florence gives you two full days -- that is not enough to even see Florence much less fill in your time with several distant day trips. With that little time, I wouldn't even do Siena and that is my favorite town in Italy.

Sienna was my favorite city in Italy.

When we went to Florence we had only 3 days and wanted to do a day trip to Sienna so after much research, we chose the tour company Walkabout Florence to book an all day excursion to Sienna, San Gimignano, Pisa which included Lunch at an organic farm. It was a fabulous day and the bus we took was really comfortable. It was a 12 hour day of walking, climbing, drinking wine, eating, gelato excursions and some great information about each town. We still talk about how much fun we had. The tour took off from the train station, which we walked to, at 7:30am and returned around 9:30pm.

Last summer myself and another traveler stayed in Florence for 4 nights and did half-day tour to Pisa, full-day tour to Cinque Terre, and half-day wine tour to San Gimignano. Personally, I think Cinque Terre and Siena is a must-see and I was pleasantly surprised with how much I enjoyed Pisa, it just depends on how badly you want to take a picture with the Leaning Tower. I would think you could do a full day Cinque Terre visit and half-day Sienna and/or Pisa and be happy! Don't forgot to spend a day walking about Florence. It was so easy to walk around and no need for any sort of public transportation